Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 7x + 6$ and $ JT = 6x + 15$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {7x + 6} = {6x + 15}$ Solve for $x$ $ x = 9$ Substitute $9$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 7({9}) + 6$ $ JT = 6({9}) + 15$ $ CJ = 63 + 6$ $ JT = 54 + 15$ $ CJ = 69$ $ JT = 69$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {69} + {69}$ $ CT = 138$